Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D5⋊#446 |
| Sylow | C5 ⋊ C2×#446 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,c^a=cg,h^a=h^2,h^c=h^3,h^d=h^4,h^f=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13016993, #13017001, #13017009, … |
| maximal normal subgroup of | #13016993, #13017001, #13017009, … |
| maximal quotient of | #13033505, #13033510, C4×#65709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19274);